Exercise
https://texercises.com/exercise/saddle/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
A system of linear differential s is given by dot x -x - y dot y -x - y abcliste abc Show that the system describes a saddle. abc Plot the direction field and add a few orbits. abcliste

Solution:
abcliste abc The system of linear differential s can be described by the matrix bf A leftmatrix- & - - & - matrixright The trace and determinant of this matrix are tau -- - Delta ----- - It follows for the eigenvalues lambda_ fractaupmsqrtdelta^-Delta frac-pmsqrt-^- - frac-pmsqrt which leads to lambda_ and lambda_-. Since one of the real eigenvalues is negative and the other positive the fixed po at the origin is a saddle. abc The diagram below shows the vector field and some orbits phase portrait. In red are the straight line solutions corresponding to the eigenvectors of the system. center includegraphicswidthtextwidth#image_path:saddle# center Almost all of the orbits start in a direction towards the origin but are finally deflected away from it. abcliste
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
Exercise:
A system of linear differential s is given by dot x -x - y dot y -x - y abcliste abc Show that the system describes a saddle. abc Plot the direction field and add a few orbits. abcliste

Solution:
abcliste abc The system of linear differential s can be described by the matrix bf A leftmatrix- & - - & - matrixright The trace and determinant of this matrix are tau -- - Delta ----- - It follows for the eigenvalues lambda_ fractaupmsqrtdelta^-Delta frac-pmsqrt-^- - frac-pmsqrt which leads to lambda_ and lambda_-. Since one of the real eigenvalues is negative and the other positive the fixed po at the origin is a saddle. abc The diagram below shows the vector field and some orbits phase portrait. In red are the straight line solutions corresponding to the eigenvectors of the system. center includegraphicswidthtextwidth#image_path:saddle# center Almost all of the orbits start in a direction towards the origin but are finally deflected away from it. abcliste
Contained in these collections:

Attributes & Decorations
Branches
Differential equations
Tags
phase portrait, saddle, vector field
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration